Invariants
| Level: | $168$ | $\SL_2$-level: | $42$ | Newform level: | $1$ | ||
| Index: | $336$ | $\PSL_2$-index: | $168$ | ||||
| Genus: | $12 = 1 + \frac{ 168 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $14^{3}\cdot42^{3}$ | Cusp orbits | $3^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 22$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 12$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 42C12 |
Level structure
| $\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}74&45\\57&17\end{bmatrix}$, $\begin{bmatrix}105&55\\41&154\end{bmatrix}$, $\begin{bmatrix}109&96\\163&131\end{bmatrix}$, $\begin{bmatrix}117&127\\118&57\end{bmatrix}$, $\begin{bmatrix}127&69\\127&68\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 84.168.12.f.1 for the level structure with $-I$) |
| Cyclic 168-isogeny field degree: | $96$ |
| Cyclic 168-torsion field degree: | $4608$ |
| Full 168-torsion field degree: | $442368$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 168.16.0-84.b.1.4 | $168$ | $21$ | $21$ | $0$ | $?$ |
| 168.168.5-21.a.1.10 | $168$ | $2$ | $2$ | $5$ | $?$ |
| 168.168.5-21.a.1.27 | $168$ | $2$ | $2$ | $5$ | $?$ |